Semiparametric inference using fractional posteriors
File(s)
Published version
Author(s)
L'Huillier, Alice
Travis, Luke
Castillo, Ismael
Ray, Kolyan
Type
Journal Article
Abstract
We establish a general Bernstein–von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for different classes of prior distributions, including Gaussian process priors. We show that fractional posterior credible sets can provide reliable semiparametric uncertainty quantification, but have inflated size. To remedy this, we further propose a shifted-and-rescaled fractional posterior set that is an efficient confidence set having optimal size under regularity conditions. As part of our proofs,
we also refine existing contraction rate results for fractional posteriors by sharpening the dependence of the rate on the fractional exponent.
we also refine existing contraction rate results for fractional posteriors by sharpening the dependence of the rate on the fractional exponent.
Date Issued
2023-01
Date Acceptance
2023-12-31
Citation
Journal of Machine Learning Research, 2023, 24 (1), pp.18619-18679
ISSN
1532-4435
Publisher
Microtome Publishing
Start Page
18619
End Page
18679
Journal / Book Title
Journal of Machine Learning Research
Volume
24
Issue
1
Copyright Statement
© 2023 Alice L’Huillier, Luke Travis, Isma¨el Castillo and Kolyan Ray.
License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided
at http://jmlr.org/papers/v24/23-0089.html.
License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided
at http://jmlr.org/papers/v24/23-0089.html.
License URL
Identifier
https://dl.acm.org/doi/abs/10.5555/3648699.3649088
Publication Status
Published
Article Number
389
Date Publish Online
2024-03-06